一句话：提出 ribbon 组合代数，证明其与 ribbon 范畴中自反对象对应，并给出迹与对偶两种等式刻画。
本文研究一类组合代数——ribbon 组合代数（带状组合代数），旨在统一解释辫状无类型线性 lambda 演算与带框定向缠结。作者证明：ribbon 范畴中的任何自反对象都给出 ribbon 组合代数；反之，由 ribbon 组合代数可构造带自反对象的 ribbon 范畴，并恢复原组合代数。证明与等式刻画依赖 Hasegawa 近期提出的内部 PRO 构造。关键结果是 ribbon 组合代数具有两种等价特征：带 trace 组合子的平衡组合代数，以及带对偶的平衡组合代数。
We investigate a class of combinatory algebras, called ribbon combinatory algebras, in which we can interpret both the braided untyped linear lambda calculus and framed oriented tangles. Any reflexive object in a ribbon category gives rise to a ribbon combinatory algebra. Conversely, From a ribbon combinatory algebra, we can construct a ribbon category with a reflexive object, from which the combinatory algebra can be recovered. To show this, and also to give the equational characterisation of ribbon combinatory algebras, we make use of the internal PRO construction developed in Hasegawa's recent work. Interestingly, we can characterise ribbon combinatory algebras in two different ways: as balanced combinatory algebras with a trace combinator, and as balanced combinatory algebras with duality.